I would argue that some did fear that he would die. The Revolution was a mess for the nobility and there were nobles interested in returning France to the Pre-Revolution state, such as the Duke of Brunswick whom made a Manifesto that declared that if the Revolution harmed the Royal family, then there be reprocussions. However this angered the Revolutionaries and when the French won at Valmy, it brought the Revolutionaries were angered enough and had enough, putting him on trial because his indifference to the Revolution and the intervention of other powers.

From what I gathered from various documentaries I always had the impression Louis knew he would die, at least when the revolution really radicalized ( not at the beginning ). I decided to try to find some articles here and there and I find one really interesting which is the report of a conference given by Philippe Pichot-Bravard, a teacher in Law History, History of Politics and History of the Church.

Source ( in French )

He says that for some time now, Louis XVI found a very deep interest in the history of Charles I of England and that he read biographies of him several times including not long before his own death. Also, though he always have been pious, Louis really turned into religion during the revolution and the " deep meaning of his role as king " which is to belong to his people entirely and be ready to sacrifice himself for the people ( according to words pronounced by his ancestor Louis XIV ).

Also, Louis XVI wrote his will in December 1792 before hearing the verdict of his trial but the will clearly shows that Louis knew he would die soon.

Here are some parts of his last will in English ( and the translation is very accurate of the original French one I just read minutes ago ) :

" [I am] involved in a trial the end of which it is impossible to foresee, on account of the passions of men "

" I hereby declare, in His [God ] presence, my last wishes and feelings.

" I die in communion with our Holy Mother, the Catholic, Apostolic, Roman Church "

Now I am pretty sure I read somewhere that Louis XVI did try to hide the truth to his son for awhile so not to worry the boy too much ( but I can't find anything to back this up so don't my word on this ). I can't tell you about how other monarchs felt though.

HERE is a translation of the will.

HERE is the original.